The ${\pi }^0-\eta -{\eta }^{\prime }$ mixing in a generalized multi-quark interaction scheme

Abstract

We investigate the isospin symmetry breaking effects within a recently derived Nambu-Jona-Lasinio related model by fitting the measured pseudoscalar meson masses and weak decay couplings $f_{\pi }$, $f_K$. Our model contains the next to leading order terms in the $1/N_c$ expansion of the effective multi-quark Lagrangian, including the ones that break the chiral symmetry explicitly. We show the important phenomenological role of these interactions: (1) they lead to an accurate fit of the low-lying pseudoscalar nonet characteristics; (2) they account for a very good agreement of the current quark masses with the present PDG values; (3) they reduce by $40\%$ the ratio $\epsilon /{\epsilon }^{\prime }$ of the ${\pi }_0-\eta$ and ${\pi }_0-{\eta }^{\prime }$ mixing angles, as compared to the case that contemplates explicit breaking only in the leading order, bringing it in consonance with the quoted values in the literature. The conventional NJL-type models fail in the joint description of these parameters.

13 pages, 8 tables, version to appear in Phys. Rev. D

References in corpus (7)

• Glueballs, Hybrids, Multiquarks. Experimental facts versus QCD inspired concepts
• A low-lying scalar meson nonet in a unitarized meson model
• Note on a sigma model connection with instanton dynamics
• Effects of eight-quark interactions on the hadronic vacuum and mass spectra of light mesons
• The eta transition form factor from space- and time-like experimental data
• Investigation of a0-f0 mixing
• Strange quark matter in the presence of explicit symmetry breaking interactions

Cited by in corpus (8)

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• Global analysis of charge exchange meson production at high energies
• Strangeness content of the pion in the U(3) Nambu-Jona-Lasinio model
• Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants
• Non-Abelian axial anomaly, axial-vector duality, and the pseudoscalar glueball
• Masses of the lowest spin-0 and spin-1 meson nonets: explicit symmetry breaking effects
• Thermodynamical properties of strongly interacting matter in a model with explicit chiral symmetry breaking interactions